The maximal order of $S(T)$

How big can $S(T):=\frac1\pi \arg \zeta(1/2+iT)$ be? Assuming the Riemann Hypothesis, it is known that $S(T)\ll \log T/\log \log T$ but that infinitely often it is bigger than $c(\log T/\log \log T)^{1/2}$ for some $c>0$ Which is closer to the truth?

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